Method of forecasting for solar-based power systems

ABSTRACT

The method of forecasting for solar-based power systems ( 10 ) recognizes that no single solar irradiance forecasting model provides the best forecasting prediction for every current weather trend at every time of the year. Instead, the method trains a classifier to select the best solar irradiance forecasting model for prevailing conditions through a machine learning approach. The resulting solar irradiance forecast predictions are then used to allocate the solar-based power systems ( 10 ) resources and modify demand when necessary in order to maintain a substantially constant voltage supply in the system ( 10 ).

TECHNICAL FIELD

The present invention relates to a method of forecasting for solar-basedpower systems, and particularly a method for forecasting solarirradiance applied to photovoltaic systems and the like.

BACKGROUND ART

The ability to forecast solar irradiance in near-real time is useful inmanaging power grid integration of renewable energy harnessed throughsuch technologies as solar heating, photovoltaics (PV), solar thermalenergy, solar architecture, and artificial photosynthesis. Solarirradiance is subject to sudden variations due to meteorological change,such as clouds, haze, and dust storms. When significant amounts of solarenergy are introduced into the power grid, sudden changes in solarirradiance can trigger grid instability. For example, a cloud formationpassing over a PV array can block up to 80% of the total irradiancereaching the PV array. Such a blockage would cause a rapid and steepfall in the power harnessed by the PV array, leading to unacceptablevoltage deviations. Solar forecasting can help solve this problem byproviding insights about forthcoming changes in solar irradiance thatcan be used to take preventive or reactive actions. Such actions mayinclude the use of other energy sources to make up for the shortage ofsolar energy, a reduction of the rate of solar energy conversion toaccommodate solar energy surplus, or storage of solar energy surplus.

Solar forecasting is typically carried out using physical or statisticalapproaches. The physical approach relies on Numerical Weather Prediction(NWP) models, which use mathematical models of the atmosphere and oceansto predict the evolution of the atmosphere from initial conditions. Thestatistical approach uses data mining techniques to train computationalmodels on historical solar irradiation data, sometimes in conjunctionwith other meteorological data. NPW models provide a useful method toforecast solar irradiance beyond six hours and up to several days ahead,but are not appropriate for higher-resolution time forecasts (e.g.,minutes) due to their coarse resolution. More specifically, the spatialand temporal granularity of even the highest resolution NWP models, suchas the North American Mesoscale Forecast System (NAM), are insufficientto resolve most clouds and any patterns with characteristic timescalesless than one hour.

Depending on the kind of instrument used in combination with statisticalmodels, one can differentiate three kind of predictions, depending onthe horizon of prediction: (1) predictions based on radiometricmeasurements can be used in combination with statistical models toobtain predictions with a temporal step from 1 second to 15 minutes anda horizon of less than 1 hour; (2) predictions based on sky cameras canbe used to obtain predictions with a temporal step from 5 minutes to 15minutes and a temporal horizon of less than 2-4 hours, depending on thelocation; and (3) satellite images can provide predictions of solarradiation with a temporal step from 5 minutes to 30 minutes, dependingon the geostationary satellite used, and a temporal horizon of less than6 hour. The predictions from these three instruments and models can besuperposed, and sometimes one can use a combination of theirpredictions. Both NWP, satellite and sky camera imaging techniques lackthe spatial and temporal resolution to provide information regardinghigh temporal frequency fluctuations of solar irradiance. An alternativeis provided through ground measurements of local meteorologicalconditions for temporal steps beyond 1 to 15 minutes.

With higher-resolution timescales, machine learning and statisticaltechniques have been shown to provide an effective methodology for solarforecasting. Various statistical and machine learning techniques havebeen used to forecast solar irradiance, including Autoregressive MovingAverage (ARMA), Autoregressive Integrated Moving Average (ARIMA),Coupled Autoregressive and Dynamical System (CARDS), Artificial NeuralNetwork (ANN), and Support Vector Regression (SVR). These algorithmshave also been successfully improved through combination with datafiltering techniques, such as wavelet transforms. For evaluationpurposes, the Persistence model, according to which no difference isassumed between current and future irradiance values, is usually used asa baseline.

One of the main problems with solar now-casting is that no singleforecasting model can consistently provide superior forecasts in allprediction instances. Evaluation of forecasting results against observeddata show that different forecasting approaches, including persistence,can rival each other across non-aggregated (e.g., minute by minute)forecast units. Thus, a method of forecasting for solar-based powersystems solving the aforementioned problems is desired.

DISCLOSURE OF INVENTION

The method of forecasting for solar-based power systems recognizes thatno single solar irradiance forecasting model provides the bestforecasting prediction for every current weather trend at every time ofthe year. Instead, the present method trains a classifier to select thebest solar irradiance forecasting model for prevailing conditionsthrough a machine learning approach. The resulting solar irradianceforecast predictions are then used to allocate the solar-based powersystems resources and modify demand when necessary in order to maintaina substantially constant voltage supply in the system.

The method of forecasting for solar-based power systems includes thefollowing steps: (a) measuring solar irradiance parameters with sensorsfor a defined geographical region over predetermined time intervals toform a data set; (b) selecting a window size defining a number of pastmeasurements and future forecast predictions to be made from the numberof past measurements; (c) partitioning the data set into successive andadjacent time series training data sequences of the selected windowsize; (d) applying each of a selected plurality of forecasting methodsto the time series training data sequences to obtain future forecastpredictions from the forecasting methods applied; (e) comparing thefuture forecast predictions of each of the forecasting methods tomeasured data to obtain a corresponding error rate associated with eachof the methods, given the time series training data sequences; (f)assigning the forecasting method with the lowest error rate as theforecasting class for the time series training data sequences; (g)repeating steps (a) through (f) to train a classifier to determine anoptimal forecasting class for different time series training datasequences; (h) using the sensors to measure current solar irradianceparameters; (i) using the classifier to determine the optimalforecasting class for the current solar irradiance parameters; (j)making future forecast predictions from the current solar irradianceparameters using the optimal forecasting class; (k) predictingsolar-based power system demands and generating capacities based uponthe future forecast predictions made in step (j); and (l) makingadjustments in the solar-based power system demands and stored energy inorder to maintain a substantially constant voltage supply for thegeographic region.

In the above method, several modeling techniques may be used as theforecasting methods, such as the aforementioned statistical and machinelearning techniques. Preferably, the Persistence technique and theSupport Vector Regression (SVR) technique are each included in theselected forecasting methods, as well as various autoregressive (AR)models for the prediction of solar radiation in the short term (i.e.,“now-casting”) using ground measurements, such as radiometricmeasurements. This allows for temporal steps of predictions of 1, 5 and10 minutes. The temporal horizon in all three cases is 15 temporal stepsahead.

These and other features of the present invention will become readilyapparent upon further review of the following specification anddrawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram illustrating system components forimplementing a method of forecasting for solar-based power systemsaccording to the present invention.

FIG. 2A is a graph illustrating autocorrelation of a one-minute timeseries used in an embodiment of the method of forecasting forsolar-based power systems.

FIG. 2B is a graph illustrating partial autocorrelation of theone-minute time series used in the embodiment of the method used in FIG.2A.

FIG. 3A is a graph illustrating autocorrelation of a five-minute timeseries used in the embodiment of the method used in FIG. 2A.

FIG. 3B is a graph illustrating partial autocorrelation of thefive-minute time series used in the embodiment of the method used inFIG. 2A.

FIG. 4A is a graph illustrating autocorrelation of a ten-minute timeseries used in the embodiment of the method used in FIG. 2A.

FIG. 4B is a graph illustrating partial autocorrelation of theten-minute time series used in the embodiment of the method used in FIG.2A.

FIG. 5 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to one-minuteaverage time series data, with the data set being recorded in January of2014.

FIG. 6 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to one-minuteaverage time series data, with a data set recorded in April of 2014.

FIG. 7 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to one-minuteaverage time series data, with a data set recorded in June of 2014.

FIG. 8 is a graph comparing relative root mean squared deviation (RMSD,%) of the autoregressive (AR) models of order 1-20 against thepersistence (PER) model, and a combination of the autoregressive modelsin an embodiment of the method of forecasting for solar-based powersystems, specifically for the one-minute time series.

FIG. 9 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to five-minuteaverage time series data, with the data set being recorded in January of2014.

FIG. 10 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to five-minuteaverage time series data, with a data set recorded in June of 2014.

FIG. 11 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to five-minuteaverage time series data, with a data set recorded in November of 2014.

FIG. 12 is a graph comparing relative root mean squared deviation (RMSD,%) of the autoregressive (AR) models of order 1-20 against thepersistence (PER) model, and a combination of the autoregressive modelsin an embodiment of the method of forecasting for solar-based powersystems, specifically for the five-minute time series.

FIG. 13 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to ten-minuteaverage time series data, with the data set being recorded in Februaryof 2014.

FIG. 14 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to ten-minuteaverage time series data, with a data set recorded in August of 2014.

FIG. 15 is a graph comparing relative root mean squared deviation (RMSD)of the autoregressive (AR) models of order 1-20 against the persistence(PER) model, and a combination of the autoregressive models in anembodiment of the method of forecasting for solar-based power systems,specifically for each horizon of prediction applied to ten-minuteaverage time series data, with a data set recorded in December of 2014.

FIG. 16 is a graph comparing relative root mean squared deviation (RMSD,%) of the autoregressive (AR) models of order 1-20 against thepersistence (PER) model, and a combination of the autoregressive modelsin an embodiment of the method of forecasting for solar-based powersystems, specifically for the ten-minute time series.

Similar reference characters denote corresponding features consistentlythroughout the attached drawings.

BEST MODES FOR CARRYING OUT THE INVENTION

The method of forecasting for solar-based power systems recognizes thatno single solar irradiance forecasting model provides the bestforecasting prediction for every current weather trend at every time ofthe year. Instead, the present method uses model evaluation data totrain a classifier that enables the selection of the best solarirradiance forecasting model for prevailing conditions through a machinelearning approach. The resulting solar irradiance forecast predictionsare then used to allocate the solar-based power systems resources andmodify demand when necessary in order to maintain a substantiallyconstant voltage supply in the system.

Generally, the method of forecasting for solar-based power systemsincludes the following steps: (a) measuring solar irradiance parameterswith sensors for a defined geographical region over predetermined timeintervals to form a data set; (b) selecting a window size defining anumber of past measurements and future forecast predictions to be madefrom the number of past measurements; (c) partitioning the data set intosuccessive and adjacent time series training data sequences of theselected window size; (d) applying each of a selected plurality offorecasting methods to the time series training data sequences to obtainfuture forecast predictions from the forecasting methods applied; (e)comparing the future forecast predictions of each of the forecastingmethods to measured data to obtain a corresponding error rate associatedwith each of the methods, given the time series training data sequences;(f) assigning the forecasting method with the lowest error rate as theforecasting class for the time series training data sequences; (g)repeating steps (a) through (f) for the selected plurality offorecasting methods and use the resulting forecasting evaluation data totrain a classifier to determine an optimal forecasting class fordifferent time series training data sequences; (h) using the sensors tomeasure current solar irradiance parameters; (i) using the classifier todetermine the optimal forecasting class for the current solar irradianceparameters; (j) making future forecast predictions from the currentsolar irradiance parameters using the optimal forecasting class; (k)predicting solar-based power system demands and generating capacitiesbased upon the future forecast predictions made in step (j); and (l)making adjustments in the solar-based power system demands and storedenergy in order to maintain a substantially constant voltage supply forthe geographic region.

In step (a) above, ground-measured solar radiation data is used tocreate data files, such as the exemplary data file shown below inTable 1. In Table 1, direct normal irradiance (DNI), global horizontalirradiance (GHI) and diffuse horizontal irradiance (DHI) are eachprovided as one-minute averages of the measured solar radiationcomponents (measured in W/m²). Each component in Table 1 was measured bya different sensor mounted on a high-precision solar radiationmonitoring station.

TABLE 1 Measured Solar Radiation Parameters YYYY-MM-DD- HH-MM DNI GHIDHI Kt Kt_p 2014-03-05-06-47 305.34 167.55 102.75 0.65 0.922014-03-05-06-48 270.89 156.47 97.45 0.60 0.84 2014-03-05-06-49 221.88141.53 91.46 0.53 0.74 2014-03-05-06-50 179.62 128.26 86.32 0.47 0.652014-03-05-06-51  84.08 105.34 82.82 0.38 0.52 2014-03-05-06-52 108.30113.37 85.17 0.40 0.55 . . . . . . . . . . . . . . . . . .2014-03-05-09-46 624.76 688.97 225.32  0.681  0.703

In the above, Kt and Kt_p are clearness indices, calculated from theground-measured GHI. Kt is the ratio of GHI to the calculated globalhorizontal radiation at the top of the atmosphere. Kt removes theseasonal dependence of GHI throughout the year. Kt_p is a modified formof Kt, which adds a correction factor for the changing atmospheric airmasses traversed by the solar radiation at any moment. Kt and Kt_p aregiven by:

$\begin{matrix}{{Kt} = \frac{GHI}{GHItoa}} & (1) \\{{Kt}_{p} = \frac{Kt}{{1.031e^{{- 1.4}/{({0.9 + {9.4/{am}}})}}} + 0.1}} & (2) \\{{{a\; m} = \frac{1}{{\cos ({SZA})} + {0.50573\left( {96.07995 - {SZA}} \right)^{- 1.6364}}}},} & (3)\end{matrix}$

where GHl_(toa) is the extraterrestrial solar radiation on a horizontalsurface at the top of the atmosphere, am is the air mass, and SZA is thesolar zenith angle in degrees. In order to ensure good accuracy in themodeling results, only measured data that pass some quality controltests should be included. For the data given above, the recommendedBaseline Surface Radiation Network quality tests were applied to allentries. Several or just a single measure of solar irradiance can beused. In the present embodiment, all examples will be given withreference to the single measure Kt_p.

Data filtering may be applied to the data set generated in step (a). Anysuitable technique, such as normalization, discretization, or waveletanalysis, used alone or in combination, may be used to remove noise fromthe data. With normalization, all numeric values in the given data setare mapped into a standard numerical interval, typically 0-1.Discretization maps continuous numeric values into discrete counterparts(e.g., high, medium, low). The wavelet transform enables thedecomposition of a time series into a time dependent sum of frequencycomponents.

In order to select the window size defining a number of pastmeasurements and future forecast predictions to be made from the numberof past measurements (step (b)), the number of steps ahead to beforecasted are first selected. Then, several data points are selected,at the beginning, middle and end of the data collection. For each datapoint, an initial training data set T is created with a window size, i,given by i=n+m, where m is the number of steps ahead to be forecasted,and n is some function over m, e.g., 3m. One or several forecastingalgorithms are then applied to T and the results are evaluated using anevaluation measure such as the Coefficient of Variation of the Root MeanSquare Error (cvRMSE) to compare predicted (pred) against observed (obs)values. Here,

${cvRMSE} = {\frac{\sqrt{\frac{\sum\limits_{t = 1}^{n}\left( {x_{{pred}_{t}} - x_{{obs}_{t}}} \right)^{2}}{n}}}{{mean}\left( {obs}_{{ti} - n} \right)}.}$

The window size, i, is successively increased and decreased until thebest evaluation results (e.g., the lowest cvRMSE) are found, todetermine the best training window size j.

In step (c), the training data is partitioned into successive andadjacent time series training data sequences of the selected windowsize. For example, if the time scale is minutes, an ideal trainingwindow size may be 180 minutes, and the time series data for Kt_p wouldbe as indicated in Table 2 below.

TABLE 2 Exemplary Partitioning of Training Data Period for Kt_pPrediction Kt_p at minute 1 . . . Kt_p at minute 180 2014-12-01-06-57→0.080137 . . . 0.067823 2014-12-01-09-56 2014-12-01-06-57→ 0.080137 . .. 0.067823 2014-12-01-09-56 2014-12-01-06-57→ 0.080137 . . . 0.0678232014-12-01-09-56 2014-12-01-06-57→ 0.080137 . . . 0.0678232014-12-01-09-56 2014-12-01-06-57→ 0.080137 . . . 0.0678232014-12-01-09-56 2014-12-01-06-57→ 0.080137 . . . 0.0678232014-12-01-09-56 . . . . . . . . . . . .

In step (d), each of a plurality of forecasting methods is applied tothe time series training data sequences to obtain future forecastpredictions from the forecasting method applied. The differentforecasting models are developed to predict n-steps ahead for the solarirradiance variable of interest, using as training data the time seriesdata developed above. In the present embodiment, two forecasting modelsare exemplified: Persistence and Support Vector Regression (SVR). Thepersistence model assumes that no change occurs from the present statethroughout the forecasting period. In SVR, within a machine learningapproach to forecasting, each training sample is a pair {{right arrowover (x)}, y}, where {right arrow over (x)} ∈

^(n) is a vector for the time-series class to be learned, and y ∈

y is the associated value. The aim of the machine learning algorithm isto find a function such that each {right arrow over (x)}_(l) in thetraining dataset approximates its value y_(i) as closely as possible.The resulting function is then used to predict values n-steps ahead ofthe time series data used for training. When the input data are amenableto linear regression, the SVR prediction function is given byy_(i)={right arrow over (w)}·{right arrow over (x_(l))}+b, where i=1, .. . , n, {right arrow over (w)} is the weight vector (i.e., a linearcombination of training patterns that supports the regression function),{right arrow over (x_(l))} is the input vector (i.e., the trainingsample), y_(i) is the value for the input vector, and b is the bias(i.e., an average over marginal vectors, which are weight vectors thatlie within the margins set by the loss function).

The objective of regression is to learn the weight vector {right arrowover (w)} that has the smallest possible length so as to avoidover-fitting. To ease the regression task, a given margin of deviation εis allowed with no penalty, and a given margin ξ is specified wheredeviation is allowed with increasing penalty. The length of the weightvector {right arrow over (w)} is obtained by minimizing the lossfunction, ½∥{right arrow over (w)}∥²+C Σ_(t=1) ^(n)(ξ_(i)+ξ*_(i))¹,subject to the constraints y_(i)−({right arrow over (w)}·{right arrowover (x)}_(l)+b)≤ε+ξ_(i), or y_(i)−({right arrow over (w)}·{right arrowover (x_(l))}+b)≥ε−ξ*_(i), for ξ_(i), ξ*_(i)≥0. The solution is given byy_(i)=Σ_(i=1) ^(n)(a_(i)−a*_(i))({right arrow over (w)}·{right arrowover (x_(l))})+b, where a_(i) and a*_(i) are Lagrange multipliers. Thetraining vectors giving nonzero Lagrange multipliers are called supportvectors and are used to construct the regression function. If the inputdata are not amenable to linear regression, then the vector data aremapped into a higher dimensional features space using a kernel functionΦ. One example is the polynomial kernel, according to which Φ({rightarrow over (w)})·Φ({right arrow over (x_(l))})=(1+{right arrow over(w)}·{right arrow over (x_(l))})³.

The forecasting models are next evaluated, using an evaluation measuresuch as cvRMSE. Forecasting evaluation results relative to eachprediction step are stored for each training data sequence (e.g., the180 minutes used above), as shown in Table 3.

TABLE 3 Forecasting Evaluation Results cvRMSE for cvRMSE for cvRMSE forcvRMSE for SVR model Persistence model SVR model Persistence modelPeriod for Kt_p at 1 at 1 at n at n Prediction step ahead step ahead . .. steps ahead steps ahead 2014-12-01-06-57→ 1.941569 3.522824 . . . . .. . . . 2014-12-01-09-56 2014-12-01-06-57→ 4.299455 8.545602 . . . . . .. . . 2014-12-01-09-56 2014-12-01-06-57→ 7.165063 14.192361 . . . . . .. . . 2014-12-01-09-56 2014-12-01-06-57→ 4.637791 14.184008 . . . . . .. . . 2014-12-01-09-56 2014-12-01-06-57→ 5.841919 5.199473 . . . . . . .. . 2014-12-01-09-56 2014-12-01-06-57→ 25.469365 15.143792 . . . . . . .. . 2014-12-01-09-56 . . . . . . . . . . . . . . . . . . . . . . . . . ..

The forecasting models are then saved as software components that takeas input a time series data sequence to output predictions for m stepsahead. Next, classification models are developed to selected the bestforecasting method. A time series data set is created that includes theevaluated forecasting models and their time series training data, asshown below in Table 4.

TABLE 4 Time Series Data Created to Train Classification Models cvRMSEfor cvRMSE for SVR model Persistence model Period for Kt_p (average over(average over Kt_p at Kt_p at Prediction all steps ahead) all stepsahead) minute 1 . . . minute 180 2014-12-01-06-57→ 1.9416 3.5228 0.0801. . . 0.2810 2014-12-01-09-56 2014-12-01-06-57→ 4.2995 8.5456 0.0801 . .. 0.2810 2014-12-01-09-56 2014-12-01-06-57→ 7.1651 14.1924 0.0801 . . .0.2810 2014-12-01-09-56 2014-12-01-06-57→ 4.6378 14.1840 0.0801 . . .0.2810 2014-12-01-09-56 2014-12-01-06-57→ 5.8419 5.1995 0.0801 . . .0.2810 2014-12-01-09-56 2014-12-01-06-57→ 25.4694 15.1438 0.0801 . . .0.2810 2014-12-01-09-56 . . . . . . . . . . . . . . . . . .

In step (f), the forecasting method with the lowest error rate isassigned as the forecasting class for the time series training datasequences. The best performing class is established as the model withthe best evaluation results; e.g., a lower cvRMSE, as shown in Table 5.

TABLE 5 Model Class Assignment to Training Records cvRMSE cvRMSE for forSVR Persistence model model (average (average Kt_p over all over all atsteps steps Kt_p at minute Model Period for Kt_p Prediction ahead)ahead) minute 1 . . . 180 Class 2014-12-01-06-57→ 1.9416 3.5228 0.0801 .. . 0.2810 SVR 2014-12-01-09-56 2014-12-01-06-57→ 4.2995 8.5456 0.0801 .. . 0.2810 SVR 2014-12-01-09-56 2014-12-01-06-57→ 7.1651 14.1924 0.0801. . . 0.2810 SVR 2014-12-01-09-56 2014-12-01-06-57→ 4.6378 14.18400.0801 . . . 0.2810 SVR 2014-12-01-09-56 2014-12-01-06-57→ 5.8419 5.19950.0801 . . . 0.2810 PER 2014-12-01-09-56 2014-12-01-06-57→ 25.469415.1438 0.0801 . . . 0.2810 PER 2014-12-01-09-56 . . . . . . . . . . . .. . . . . .

Additional data filtering processes may be applied to the above dataset. Data can be filtered using any suitable filtering techniques, suchas discretization, normalization or wavelet transforms, or a combinationof these. The data is then used to train a classification model capableof recognizing the highest ranking model given an input time seriestraining data sequence. A number of machine learning algorithms can beused to train a classifier from data, such as, for example, thedecision-tree classification algorithm. In decision-tree classification,the model identifies members of a class as the result of a sequence ofdecisions. A decision tree typically consists of two types of nodes:test nodes and prediction nodes. The test node describes the conditionthat must be met in order to make a decision. Several test nodes canoccur in a sequence to indicate the number of decisions that must betaken and the order in which these decisions follow one another to reacha prediction outcome.

A decision tree classifier is “learned” from a training dataset by amodel which establishes the sequential order of test nodes according tohow informative the nodes' attributes are. The model determines theinformation content of an attribute by its information gain with respectto the classification tasks. The information gain of an attribute withrespect to a class is the reduction in entropy (i.e., the uncertainty)of the value for the class the value of the attribute is known. The testnodes with more informative attributes occur earlier in the decisiontree. The model creates test nodes using the available attributes untilall data in the training dataset have been accounted for. Typically, notall attributes are used because decision tree learners use pruningstrategies to reduce the number of nodes. The number of attributesdepends on the specific implementation. The “alternating decision treealgorithm” uses a machine learning meta-algorithm, called “boosting”, tominimize the number of nodes without losing accuracy. It should beunderstood that any suitable classification algorithm may be used, suchas, for example, Bayesian nets, Support Vector Machines, boosting, NaïveBayes, bagging, random forest and Model Trees. The classification modelis saved as a software component capable of recognizing the highestranking model given an input time series training data sequence.

It should be understood that the calculations may be performed by anysuitable computer system, such as that diagrammatically shown in FIG. 1.Data is entered into system 10 via any suitable type of user interface16, and may be stored in memory 12, which may be any suitable type ofcomputer readable and programmable memory and is preferably anon-transitory, computer readable storage medium. Calculations areperformed by processor 14, which may be any suitable type of computerprocessor and may be displayed to the user on display 18, which may beany suitable type of computer display. Sensor data is collected fromsolar irradiance sensors 20, such as, for example, satellite and skycameras, radiometric sensors, pyrheliometers, pyranometers and the like.

Processor 14 may be associated with, or incorporated into, any suitabletype of computing device, for example, a personal computer or aprogrammable logic controller. The display 18, the processor 14, thememory 12 and any associated computer readable recording media are incommunication with one another by any suitable type of data bus, as iswell known in the art.

Examples of computer-readable recording media include non-transitorystorage media, a magnetic recording apparatus, an optical disk, amagneto-optical disk, and/or a semiconductor memory (for example, RAM,ROM, etc.). Examples of magnetic recording apparatus that may be used inaddition to memory 112, or in place of memory 12, include a hard diskdevice (HDD), a flexible disk (FD), and a magnetic tape (MT). Examplesof the optical disk include a DVD (Digital Versatile Disc), a DVD-RAM, aCD-ROM (Compact Disc-Read Only Memory), and a CD-R (Recordable)/RW. Itshould be understood that non-transitory computer-readable storage mediainclude all computer-readable media, with the sole exception being atransitory, propagating signal.

In the above method, the Persistence technique and the Support VectorRegression (SVR) technique may be used as the forecasting methods. As analternative, the Persistence model may be replaced by autoregressive(AR) models, particularly for the prediction of solar radiation in theshort term (i.e., “now-casting”) using ground measurements, such asradiometric measurements. This allows for temporal steps of predictionsof 1, 5 and 10 minutes. The temporal horizon in all three cases is 15temporal steps ahead. In the below, due to non-stationary behavior,global solar irradiance has been transformed to a normalized clearnessindex K*_(T). The clearness index is defined as the ratio between groundmeasured global solar irradiance and extraterrestrial solar irradiance,including a correction for air mass.

Autoregressive models generate lineal predictions from the input and arealso known as Infinite Impulse Response Filters (IIRFs). The notationAR(p) refers to the autoregressive model of order p. The AR(p) isexpressed by the following equation:

{circumflex over (x)} _(t) =c+Σ _(i=1) ^(p) a _(i) x _(t−i)+ε_(t),

where a_(i) are the parameters of the model, c is a constant whichrepresents the mean value of the time series, and ε_(t) is a white noisesignal. As will be discussed in greater detail below, twenty differentautoregressive models AR(p) have been tested, with order p=1, . . . , 20for 1, 5 and 10 minutes average time series. Exemplary data are from theQatar Environment and Energy Research Institute (QEERI), which has beenoperating a high precision solar radiation monitoring station since theend of November 2012 in Education City, Doha (25.33° N, 51.43° E). Thestation is equipped with a solar tracker with a sun sensor kit, forimproved tracking accuracy, and a shading ball assembly for diffusemeasurements. Mounted on the sun tracker are one first classpyrheliometer for measuring Direct Normal Irradiance (DNI), and twosecondary standard pyranometers (one of them shaded) for GlobalHorizontal Irradiance (GHI) and Diffuse Horizontal Irradiance (DHI)measurements. Both pyranometers are fitted with ventilation units. Datafrom the monitoring station are sampled every second and recorded asminute averages in W/m².

FIGS. 2A and 2B show autocorrelation and partial autocorrelation of aone-minute time series used in the alternative embodiment of the methodof forecasting for solar-based power systems, respectively. Similarly,FIGS. 3A and 3B show autocorrelation and partial autocorrelation of afive-minute time series, respectively, and FIGS. 4A and 4B showautocorrelation and partial autocorrelation of a ten-minute time series.The metrics to measure the errors rates of the models are the mean biasdeviation (MBD), the relative root mean squared deviation (RMSD) and itsrelative values rMBD and rRMSD normalized with the mean value of theobserved variable to predict for the period under validation.

The present models are compared with a baseline model, with theintention of measuring the improvement achieved. The basic model chosenis the persistence model (PER) because it is the most extended model tocontrast new proposed models. As described above, persistence is basedon the assumption that the value for the next temporal step is the sameas the present value: {circumflex over (x)}_(t+k)=x_(t), where{circumflex over (x)}_(t+k) is the prediction for the next k steps, andx_(t) is the observation at the temporal instant t.

FIG. 5 is a graph comparing relative root mean squared deviation (RMSD)of the autocorrelation (AR) model against the persistence (PER) model,and a combination autocorrelation model in the alternative embodiment ofthe method of forecasting for solar-based power systems, specificallyfor each horizon of prediction applied to one-minute average time seriesdata (taken from January of 2014). The new “AR combined” model(AR_COMB_MIN) is detailed below. FIGS. 6 and 7 show similar comparisonsfor data sets recorded in April of 2014 and June of 2014, respectively.

Analysis of this data shows that there is a dependence on the horizon ofprediction and the complexity of the AR models which provide the minimumerror. For each horizon n, the best results in terms of minimum rRMSDare obtained with an AR model of order (n+1)[AR (n+1)]. This is the “ARcombined” model (AR_COMB_MIN) noted above. The same behavior is alsoobserved in the 5 and 10 minutes time series. Table 6 shows MBD, RMSD,rMBD and rRMSD results for the AR, PER and AR-combined models with theone-minute time series from 2014.

TABLE 6 MBD, RMSD, rMBD and rRMSD Results for AR, PER and AR-combinedModels with One-minute Time Series Model MBD RMSD rMBD(%) rRMSD(%) AR(1)−0.01 0.06 −0.84 9.44 AR(2) −0.01 0.06 −0.81 8.76 AR(3) 0.00 0.06 −0.598.26 AR(4) 0.00 0.05 −0.50 7.91 AR(5) 0.00 0.05 −0.43 7.63 AR(6) 0.000.05 −0.39 7.40 AR(7) 0.00 0.05 −0.35 7.24 AR(8) 0.00 0.05 −0.31 7.12AR(9) 0.00 0.05 −0.28 7.01 AR(10) 0.00 0.05 −0.26 6.94 AR(11) 0.00 0.05−0.24 6.90 AR(12) 0.00 0.05 −0.23 6.91 AR(13) 0.00 0.05 −0.21 6.99AR(14) 0.00 0.05 −0.21 7.07 AR(15) 0.00 0.05 −0.20 7.24 AR(16) 0.00 0.05−0.18 7.51 AR(17) 0.00 0.05 −0.18 7.78 AR(18) 0.00 0.05 −0.17 8.04AR(19) 0.00 0.06 −0.17 8.09 AR(20) 0.00 0.05 −0.17 8.04 PER 0.00 0.060.13 9.42 AR_COMB_MIN 0.00 0.02 −0.26 3.30

FIG. 8 shows model rRMSD results for the one-minute time series for eachtemporal horizon of prediction. The above data shows that theAR-combined model is better than any other model, including the PERbaseline model. The difference is quite considerable during the entireyear, except in June. The lower limit of monthly rRMSD is around 6%.FIG. 9 is a graph comparing relative root mean squared deviation (RMSD)of the autocorrelation (AR) model against the persistence (PER) model,and a combination autocorrelation model in the alternative embodiment ofthe method of forecasting for solar-based power systems, specificallyfor each horizon of prediction applied to the five-minute average timeseries data (taken from January of 2014). FIGS. 10 and 11 show similarcomparisons for data sets recorded in June of 2014 and November of 2014,respectively.

Table 7 shows MBD, RMSD, rMBD and rRMSD results for the AR, PER andAR-combined models with the five-minute time series from 2014.

TABLE 7 MBD, RMSD, rMBD and rRMSD Results for AR, PER and AR-combinedModels with Five-minute Time Series Model MBD RMSD rMBD(%) rRMSD(%)AR(1) −0.01 0.09 −0.96 13.38 AR(2) 0.00 0.08 −0.56 12.46 AR(3) 0.00 0.08−0.14 11.89 AR(4) 0.00 0.08 0.05 11.53 AR(5) 0.00 0.08 0.19 11.28 AR(6)0.00 0.08 0.26 11.14 AR(7) 0.00 0.07 0.32 11.08 AR(8) 0.00 0.08 0.3411.11 AR(9) 0.00 0.08 0.36 11.22 AR(10) 0.00 0.08 0.37 11.38 AR(11) 0.000.08 0.38 11.55 AR(12) 0.00 0.08 0.38 11.77 AR(13) 0.00 0.08 0.38 12.01AR(14) 0.00 0.08 0.38 12.29 AR(15) 0.00 0.09 0.39 12.62 AR(16) 0.00 0.090.41 13.02 AR(17) 0.00 0.09 0.40 13.41 AR(18) 0.00 0.09 0.39 13.82AR(19) 0.00 0.10 0.38 14.21 AR(20) 0.00 0.10 0.39 14.58 PER 0.01 0.091.30 13.40 AR_COMB_MIN 0.00 0.05 0.33 7.72

FIG. 12 shows model rRMSD results for the five-minute time series foreach temporal horizon of prediction. From the above data, one canconclude that the AR-combined model outperforms the other models and thePER baseline model for the case of a five-minute average time series.The difference is quite considerable during the entire year, except inJune. The lower limit of monthly rRMSD is around 6%.

FIG. 13 is a graph comparing relative root mean squared deviation (RMSD)of the autocorrelation (AR) model against the persistence (PER) model,and the combination autocorrelation model in the alternative embodimentof the method of forecasting for solar-based power systems, specificallyfor each horizon of prediction applied to the ten-minute average timeseries data (taken from February of 2014). FIGS. 14 and 15 show similarcomparisons for data sets recorded in August of 2014 and December of2014, respectively.

Table 8 shows MBD, RMSD, rMBD and rRMSD results for the AR, PER andAR-combined models with the ten-minute time series from 2014.

TABLE 8 MBD, RMSD, rMBD and rRMSD Results for AR, PER and AR-combinedModels with Ten-minute Time Series Model MBD RMSD rMBD(%) rRMSD(%) AR(1)0.00 0.09 −0.23 16.26 AR(2) 0.00 0.08 0.26 15.19 AR(3) 0.01 0.08 0.7214.60 AR(4) 0.01 0.08 0.89 14.23 AR(5) 0.01 0.08 0.95 14.02 AR(6) 0.010.08 0.96 13.93 AR(7) 0.01 0.08 0.90 13.90 AR(8) 0.01 0.08 0.88 13.95AR(9) 0.01 0.08 0.85 14.04 AR(10) 0.01 0.08 0.77 14.18 AR(11) 0.01 0.080.73 14.41 AR(12) 0.01 0.08 0.68 14.70 AR(13) 0.01 0.08 0.65 15.07AR(14) 0.01 0.09 0.61 15.48 AR(15) 0.00 0.09 0.60 15.93 AR(16) 0.00 0.090.61 16.40 AR(17) 0.00 0.09 0.62 16.89 AR(18) 0.00 0.10 0.60 17.27AR(19) 0.00 0.10 0.58 17.69 AR(20) 0.00 0.10 0.55 18.10 PER 0.02 0.102.62 16.39 AR_COMB_MIN 0.01 0.06 0.61 10.18

FIG. 16 shows model rRMSD results for the ten-minute time series foreach temporal horizon of prediction. From the above data, one canconclude that the AR-combined model is better than any AR model and thePER model, also for the case of 10 minute average time series. Thedifference is quite considerable during the entire year, except in June.This is due to the fact that June is a month where there are almost noclouds in Qatar and almost no impact in lower variability of solarradiation. The lower limit of monthly rRMSD is around 9%.

It is to be understood that the present invention is not limited to theembodiments described above, but encompasses any and all embodimentswithin the scope of the following claims.

1. A method of forecasting for solar-based power systems, comprising thesteps of: (a) measuring solar irradiance parameters with sensors for adefined geographical region over predetermined time intervals to form adata set; (b) selecting a window size defining a number of pastmeasurements and future forecast predictions to be made from the numberof past measurements; (c) partitioning the data set into successive andadjacent time series training data sequences of the selected windowsize; (d) applying a plurality of forecasting methods to the time seriestraining data sequences to obtain future forecast predictions from eachof the forecasting methods; (e) comparing the future forecastpredictions of each of the forecasting methods to measured data toobtain a corresponding error rate associated with each of the methods,given the time series training data sequences; (f) assigning theforecasting method with the lowest error rate as the forecasting classfor the time series training data sequences; (g) repeating steps (a)through (f) to train a classifier to determine an optimal forecastingclass for different time series training data sequences; (h) using thesensors to measure current solar irradiance parameters; (i) using theclassifier to determine the optimal forecasting class for the currentsolar irradiance parameters; (j) making future forecast predictions fromthe current solar irradiance parameters using the optimal forecastingclass; (k) predicting solar-based power system demands and generatingcapacities based upon the future forecast predictions made in step (j);and (l) making adjustments in the solar-based power system demands andstored energy in order to maintain a substantially constant voltagesupply for the geographic region.
 2. The method of forecasting forsolar-based power systems as recited in claim 1, wherein the step ofmeasuring solar irradiance parameters comprises measuring direct normalirradiance (DNI), global horizontal irradiance (GHI) and diffusehorizontal irradiance (DHI).
 3. The method of forecasting forsolar-based power systems as recited in claim 2, wherein the step ofmeasuring solar irradiance parameters comprises measuring the solarirradiance parameters in one minute intervals.
 4. The method offorecasting for solar-based power systems as recited in claim 1, furthercomprising the step of applying data filtering to the data set generatedin step (a).
 5. The method of forecasting for solar-based power systemsas recited in claim 1, wherein the plurality of forecasting methodscomprise a persistence method and a support vector regression method. 6.A method of forecasting for solar-based power systems, comprising thesteps of: measuring solar irradiance parameters with sensors for adefined geographical region over predetermined time intervals to form adata set; selecting a window size defining a number of past measurementsand future forecast predictions to be made from the number of pastmeasurements; partitioning the data set into successive and adjacenttime series training data sequences of the selected window size;applying an autoregressive forecasting method to the time seriestraining data sequences to obtain future forecast predictions;predicting solar-based power system demands and generating capacitiesbased upon the future forecast predictions; and making adjustments inthe solar-based power system demands and stored energy in order tomaintain a substantially constant voltage supply for the geographicregion.